最小非厄米三聚体中的潜在对称性
Latent symmetry in a minimal non-Hermitian trimer
AI总结：
研究由共谱位点对嵌入非互易耦合三站点网络形成的最小非厄米三聚体，揭示共谱性提供结构潜在对称约束，而精确暗态解耦需要额外代数匹配条件，并展示暗态兼容代表类可分解为暗亮扇区，亮扇区在特定参数下具有PT对称性和部分谱实性，临界点处出现二阶异常点。
摘要：
我们研究了一个由共谱位点对嵌入具有非互易耦合的三站点网络形成的最小非厄米三聚体中的潜在对称性。我们表明，共谱性提供了一个结构性的潜在对称约束，而精确的暗态解耦需要耦合之间的额外代数匹配条件。对于该共谱类的一个暗态兼容代表，模型允许精确分解为暗扇区和亮扇区：暗模在谱上孤立并保留复本征值，而亮扇区约化为一个有效的非厄米二聚体。对于合适的参数选择，这个约化子系统变为$\mathcal{PT}$对称并表现出部分谱实性，两个实本征值与复暗本征值共存。在临界点处，亮扇区包含一个嵌入的二阶异常点，这使得整个三聚体有缺陷并产生特征性的约当块动力学。这些结果确立了非厄米三聚体作为一个最小解析可解设置，其中潜在对称性、扇区分辨的$\mathcal{PT}$对称性和异常点物理自然共存。
英文摘要：
We study a minimal non-Hermitian trimer with latent symmetry formed by a cospectral pair of sites embedded in a three-site network with nonreciprocal couplings. We show that cospectrality provides a structural latent-symmetry constraint, whereas exact dark-state decoupling requires an additional algebraic matching condition among the couplings. For a dark-state-compatible representative of this cospectral class, the model admits an exact decomposition into dark and bright sectors: the dark mode is spectrally isolated and retains a complex eigenvalue, while the bright sector reduces to an effective non-Hermitian dimer. For a suitable choice of parameters, this reduced subsystem becomes $\mathcal{PT}$-symmetric and exhibits partial spectral reality, with two real eigenvalues coexisting with the complex dark eigenvalue. At the critical point, the bright sector hosts an embedded second-order exceptional point, which renders the full trimer defective and gives rise to the characteristic Jordan-block dynamics. These results establish the non-Hermitian trimer as a minimal analytically solvable setting in which latent symmetry, sector-resolved $\mathcal{PT}$ symmetry, and exceptional-point physics naturally coexist.
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